Grain size quantification method for thick plate structures based on wake waves

Abstract

The present invention proposes a method for quantifying the grain size of thick plate structures based on wake waves, which belongs to the field of grain size quantification of thick plate structures, and includes: S1, performing pulse signal excitation on the thick plate structure and collecting wake wave signals; S2, obtaining a preliminary noise reduction signal based on the collected wake wave signals; S3, performing variational modal decomposition on the preliminary noise reduction signal to extract a finite bandwidth signal with a specific frequency; S4, fitting the attenuation coefficient using the average power envelope of the finite bandwidth signal; S5, using a logarithmic linear quantization model to obtain a grain size quantization result that takes uncertainty into account. The present invention utilizes the characteristics of wake waves to accurately and quickly quantify the grain size of thick plate structures with large frequency-thickness products; the average power envelope effectively describes the overall energy attenuation law related to the signal and the grain size, and the obtained wake wave attenuation coefficient can be used to accurately and reliably quantify the grain size of the thick plate structure, ensuring the accuracy of the prediction results.

Description

Technical Field

[0001] The present invention belongs to the technical field of thick plate structure grain size quantification, and in particular relates to a thick plate structure grain size quantification method based on wake waves. Background Art

[0002] Ensuring that the mechanical properties of structures meet service requirements is one of the core safeguards for the safe service of critical components. As a key microstructural parameter affecting the tensile strength and fatigue resistance of materials, accurate quantification of grain size is an essential foundation for improving the quality of key components and reducing development costs. Traditional grain size assessment relies primarily on time-consuming and costly destructive testing methods, such as metallography and electron backscatter diffraction, which are difficult to meet the needs of actual engineering applications. In contrast, ultrasonic nondestructive testing technology has become a research hotspot in the field of grain size quantification due to its high efficiency and low cost. When propagating in polycrystalline materials, ultrasonic waves interact with grain boundaries and cause scattering, which in turn causes the ultrasonic energy to gradually attenuate and the signal characteristics to change. Ultrasonic signal characteristics such as attenuation, backscattered signal, and wave velocity have been shown to be correlated with grain size. Among them, attenuation is generally the preferred signal characteristic in industrial practice due to its intuitive principle and simple evaluation.

[0003] Depending on the thickness of the target structure and the combination of ultrasonic frequencies (i.e., different frequency-thickness products), ultrasonic waves will exhibit various propagation modes, represented by bulk waves and guided waves. Currently, grain size quantification methods based on ultrasonic bulk waves and guided waves have been applied in specific industrial scenarios for different product types and diverse industrial inspection requirements. Ultrasonic bulk waves are typically used at high frequencies and thickness products, propagating within the material volume and achieving high spatial resolution. However, traditional bulk wave methods have the following limitations: First, insufficient frequency-thickness products lead to increased signal analysis complexity; second, excessively high frequencies increase the difficulty of grain size quantification; third, bulk waves can only analyze localized grain information at a single measurement location, requiring dense sampling for large-scale structure assessment, resulting in low inspection efficiency. Guided waves propagate along thin plate structures with low frequencies and thickness products, enabling efficient inspection of structures over a wide area. However, high frequency-thickness products lead to complex propagation modes and difficulty in analysis. In summary, determining the appropriate ultrasonic bulk wave or guided wave method for grain size assessment in thick plate structures, a common practice in engineering, is challenging.

[0004] When the frequency-thickness product in a plate structure exceeds 15MHz·mm, a wake wave will form in the structure, manifesting as a series of trailing pulses in the ultrasonic signal. The characteristics of the wake wave are between those of bulk waves and guided waves, with a short wavelength and long-distance propagation characteristics similar to guided waves. It achieves an effective balance between high resolution and detection efficiency, and shows good engineering application potential in the detection of thick plate structures. However, the complex propagation mechanism of the wake wave poses a challenge to the applicability of existing signal processing methods. Currently, a general method for quantifying grain size using wake waves has not yet been developed. In response to the engineering needs of quantifying grain size in thick plate materials, the study of ultrasonic detection methods based on the attenuation characteristics of wake waves can overcome the limitations of traditional bulk wave and guided wave methods in the detection of thick plate structures, achieve efficient and accurate grain size quantification, and has important application value and research significance. Summary of the Invention

[0005] In response to the above-mentioned deficiencies in the existing technologies, the present invention proposes a method for quantifying the grain size of thick plate structures based on wake waves. First, an ultrasonic quantification system for the grain size of thick plate structures is established, and an ultrasonic transducer is used to pulse excite the thick plate structure to be detected and collect wake wave signals. Based on the characteristics of the wake wave signal, a two-step signal denoising method is adopted, including cross-correlation calculation with the excitation pulse and filtering the signal using a variational mode decomposition method to obtain a time-domain finite bandwidth signal. Subsequently, the attenuation law of the finite bandwidth signal after noise reduction is analyzed based on the average power envelope, thereby evaluating the attenuation coefficient of the wake wave in the thick plate structure. Finally, based on the logarithmic linear quantification model between the attenuation coefficient and the grain size, the uncertainty quantification result of the grain size is obtained. Compared with existing grain size quantification methods based on ultrasonic body waves and guided waves, the present invention is more suitable for the evaluation of thick plate structures, has higher detection efficiency, lower analysis complexity, and is easy to use. The obtained grain quantification results are highly accurate and robust.

[0006] Specifically, the present invention provides a method for quantifying grain size of thick plate structure based on wake wave, which comprises the following steps:

[0007] S1. Build an ultrasonic quantification system for grain size of thick plate structures, apply pulse signal excitation to the thick plate structures and collect wake wave signals;

[0008] S2. Perform cross-correlation operation on the collected tail wave signal f(τ) and the excitation pulse g(τ) to obtain a preliminary noise reduction signal. The calculation formula is as follows:

[0009]

[0010] Among them, τ is the time variable and t is the time shift variable;

[0011] S3, perform variational mode decomposition on the preliminary denoised signal R(t), and decompose the signal into k modes with different center frequencies ω i The bandwidth-limited intrinsic mode function s i (t), preliminary noise reduction signal R(t) and limited bandwidth intrinsic mode function s i (t) have the following relationship:

[0012]

[0013] Among them, s r (t) is the residual signal. According to the center frequency ω0 of the excitation pulse, the center frequency ω is selected from the k finite bandwidth natural mode functions. i The finite bandwidth intrinsic mode function s with the smallest deviation from ω0 i (t) as a bandwidth-limited signal I(t);

[0014] S4. Fitting the attenuation coefficient using the average power envelope of the bandwidth-limited signal. This step includes the following sub-steps:

[0015] S41. For different time-shift variables t, calculate the average power of the bandwidth-limited signal I(t) within the time window [t, t+T] with a width of T, and obtain the average power envelope curve of the bandwidth-limited signal. The calculation formula is as follows:

[0016]

[0017] Where u is the time variable in the time window [t, t+T];

[0018] S42, based on the obtained average power envelope curve, fitting using an e-exponential decay model to obtain an attenuation coefficient α;

[0019] The calculation formula of the attenuation coefficient α is as follows:

[0020] E(t)=E0e (-αt) (4)

[0021] Where E0 is the fitting parameter representing the initial power; the starting time of the data used for fitting is the time of the first peak of the average power envelope; the ending time is the first inflection point of the average power envelope, that is, the time when the slope first reaches 0; if the average power envelope continues to decay over the entire recorded time range, all data after the maximum average power are used for fitting;

[0022] S5. Based on the wake wave attenuation coefficient obtained in step S4, a log-linear quantization model is used to obtain a grain size quantification result taking uncertainty into account. This step includes the following sub-steps:

[0023] S51, constructing a logarithmic linear quantization model, and obtaining a logarithmic quantization result of the grain size according to the logarithmic linear quantization model;

[0024] S52. Calculate the probability density function of the logarithmic grain size, obtain multiple sets of logarithmic grain sizes using a logarithmic linear quantization model, and fit the probability density function of the logarithmic grain size using a normal distribution:

[0025]

[0026] Among them, μ and σ 2 are the mean and variance of the normal distribution respectively. According to the probability density function, the probability distribution of the predicted grain size considering the uncertainty is obtained. The mean of the probability distribution of the grain size is the predicted value of the grain size.

[0027] Preferably, the log-linear quantization model in step S51 is as follows:

[0028] ln d=m1+m2 lnα (5)

[0029] Where d is the grain size quantification result, m1 and m2 are the first fitting parameter and the second fitting parameter of the log-linear quantization model obtained based on the wake wave experimental evaluation of the same material, and obey the multivariate normal distribution MVN(M, ∑), where M is the mean vector and ∑ is the covariance matrix.

[0030] Preferably, in step S52, considering the uncertainty of the model parameters, the first fitting parameter m1 and the second fitting parameter m2 are sampled according to the multivariate normal distribution MVN(M, ∑), and based on the solved attenuation coefficient α, the logarithmic grain size is obtained by using the combination of different first fitting parameters m1 and second fitting parameters m2 obtained by sampling using the logarithmic linear quantization model.

[0031] Preferably, in step S1, the pulse signal is used to excite the thick plate structure to be measured and the wake wave signal is collected, which specifically includes the following steps:

[0032] S11, placing an ultrasonic transducer on the target area surface of the thick plate structure to be measured;

[0033] S12, controlling the output end of the pulse generator to generate a narrowband sinusoidal wave pulse as an input excitation signal for the ultrasonic transducer, and simultaneously generating a synchronization signal from the synchronization output end and connecting the synchronization signal to the synchronization input end of the oscilloscope;

[0034] S13. The center frequency of the excitation pulse is determined based on the thickness of the thick plate structure to be measured, the wave velocity and the estimated grain size range, so that the frequency-thickness product is greater than 15 MHz·mm;

[0035] S14. Using an oscilloscope, based on the synchronization signal of the synchronization input terminal as a trigger signal, synchronously collects the tail wave signal received by the ultrasonic transducer and transmits it to the upper controller.

[0036] Preferably, the tail wave signal used for cross-correlation calculation in step S2 is the signal after removing the initial crosstalk portion of the signal.

[0037] Preferably, the constrained variational problem to be constructed in the variational modal decomposition in step S3 is:

[0038]

[0039] Where δ(t) is the Dirac delta function, j is the imaginary unit, i = 1, ..., k, and by introducing the quadratic penalty term β and the Lagrange multiplier λ, the constrained problem is transformed into the following unconstrained problem:

[0040]

[0041] Among them, L({s i},{ω i},λ) is the augmented Lagrangian function.

[0042] The above optimization problem is solved iteratively to obtain k finite bandwidth intrinsic mode functions s i (t).

[0043] Preferably, in step S4, different times t for evaluating the average power are selected at a certain time interval Δt.

[0044] Preferably, the time window width T used for evaluating the average power in step S4 includes multiple reflected wave packets.

[0045] Preferably, in step S4, the curve is average-smoothed, thereby suppressing local noise in the average power envelope curve.

[0046] Preferably, in step S5, the first fitting parameter and the second fitting parameter of the model and their respective distributions are determined using a plurality of thick plate specimens having the same thickness and material as the thick plate structure to be measured but with different grain sizes.

[0047] Compared with the prior art, the beneficial technical effects of the present invention are:

[0048] (1) The wake wave-based grain size quantification method for thick plate structures proposed in this invention utilizes the short wavelength and long-distance propagation characteristics of wake waves to overcome the detection limitations of traditional body wave and waveguide technologies for thick plate structures, and is conducive to accurate and rapid grain size quantification of thick plate structures with large frequency-thickness products. The overall energy attenuation law related to the signal and grain size is effectively described by the average power envelope, and the obtained wake wave attenuation coefficient can be used to accurately and reliably quantify the grain size of thick plate structures.

[0049] (2) The two-step signal denoising method proposed in the present invention simplifies the attenuation characteristic analysis process of complex wake wave signals, wherein the cross-correlation operation with the excitation pulse effectively suppresses the incoherent noise, and the variational mode decomposition decomposes the signal into simple finite bandwidth signals while retaining the key attenuation characteristics; by extracting finite bandwidth signals with similar frequency components for subsequent attenuation analysis, the quantization error caused by the frequency difference of different specimens can be reduced, thereby improving the accuracy and robustness of grain size quantization. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0051] Figure 1 This is a flow chart of the method for lossless quantification of grain size of thick plate structure based on wake wave of the present invention;

[0052] Figure 2 1. It is a schematic diagram of the ultrasonic quantification system and process flow of the thick plate structure in an embodiment of the present invention;

[0053] Figure 3 1 is a schematic diagram of the waveform and power spectrum density of the excitation signal in an embodiment of the present invention;

[0054] Figure 4 1 is a schematic diagram of the waveform and power spectrum density of the wake wave signal in the thick plate structure collected in an embodiment of the present invention;

[0055] Figure 5 1 is a schematic diagram of the waveform and power spectrum density of the tail wave signal cross-correlation calculation result in an embodiment of the present invention;

[0056] Figure 6 1 is a schematic diagram of the waveform and power spectrum density of the variational modal decomposition processing result of the noise reduction signal in an embodiment of the present invention;

[0057] Figure 7 1 is a schematic diagram of average power envelope fitting of a bandwidth-limited signal in an embodiment of the present invention;

[0058] Figure 8It is the probability density function result of the quantification of the grain size of the thick plate structure obtained in the embodiment of the present invention. DETAILED DESCRIPTION

[0059] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the relevant invention are shown in the accompanying drawings.

[0060] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0061] The present invention proposes a method for quantifying the grain size of thick plate structures based on wake waves, such as Figure 1 As shown, the method includes the following steps:

[0062] S1. Build an ultrasonic quantification system for grain size of thick plate structures, using pulse signals to excite and collect wake wave signals.

[0063] like Figure 2 As shown in Figure 1, the ultrasonic grain size quantification system for thick plate structures includes a pulse generator, an ultrasonic transducer, an oscilloscope, and a host controller. The pulse generator generates a pulsed excitation electrical signal, the output of which is transmitted via a wire to the excitation terminal of the ultrasonic transducer, generating ultrasonic waves in the thick plate structure to be measured. The receiving terminal of the ultrasonic transducer collects the ultrasonic waves from the structure and forms an electrical signal, which is connected to the input terminal of the oscilloscope via a wire and collected. The synchronous output terminal of the pulse generator is connected to the synchronous input terminal of the oscilloscope to ensure synchronization between different devices. The host controller is used to adjust the output signal of the pulse generator and record the collected signal of the oscilloscope for analysis.

[0064] Acquiring ultrasonic wake wave signals specifically includes the following sub-steps:

[0065] S11. Arrange an ultrasonic transducer on the surface of a target area of ​​the thick plate structure to be measured.

[0066] S12. The output end of the control pulse generator generates a narrowband sinusoidal wave pulse as an input excitation signal for the ultrasonic transducer. At the same time, a synchronization signal is generated from the synchronization output end and connected to the synchronization input end of the oscilloscope.

[0067] S13. The center frequency of the excitation pulse is determined based on the thickness of the thick plate structure to be measured, the wave velocity, and the estimated grain size range, so that the frequency-thickness product is greater than 15 MHz·mm to ensure the formation of a wake wave in the structure and improve the accuracy of grain size measurement.

[0068] S14. Using an oscilloscope, based on the synchronization signal of the synchronization input terminal as a trigger signal, synchronously collects the tail wave signal received by the ultrasonic transducer and transmits it to the upper controller.

[0069] S2. After removing the initial crosstalk of the signal, perform cross-correlation operation on the collected tail wave signal f(τ) and the excitation pulse g(τ) to obtain the preliminary noise reduction signal. The calculation formula is as follows:

[0070]

[0071] Among them, τ is the time variable and t is the time shift variable, both of which represent time.

[0072] S3. Perform variational mode decomposition on the preliminary noise reduction signal R(t) to extract a limited bandwidth signal with a specific frequency. This step includes the following sub-steps:

[0073] S31. Construct the following constrained variational problem: decompose the signal into k components with different center frequencies ω. i The bandwidth-limited intrinsic mode function s i (t), as follows:

[0074]

[0075] Where δ(t) is the Dirac delta function, j is the imaginary unit, i = 1, ..., k. By introducing the quadratic penalty term β and the Lagrange multiplier λ, the constrained problem is transformed into the following unconstrained problem:

[0076]

[0077] The above optimization problem is solved iteratively to obtain k finite bandwidth intrinsic mode functions s i (t), and the following relationship exists:

[0078]

[0079] Among them, s r (t) is the residual signal.

[0080] S32, according to the center frequency ω0 of the excitation pulse, select the center frequency ω from the k limited bandwidth natural mode functions i The bandwidth intrinsic mode function s of the finite bandwidth signal with the smallest deviation from ω0 i (t) as I(t).

[0081] S4. Fitting the attenuation coefficient using the average power envelope of the bandwidth-limited signal. This step includes the following sub-steps:

[0082] S41. At different times t, calculate the average power of the bandwidth-limited signal I(t) within a time window [t, t+T] with a width of T to obtain an average power envelope curve of the bandwidth-limited signal. The calculation formula is as follows:

[0083]

[0084] Where y is the time variable within the time window [t, t+T]. The width of the time window T should include multiple reflected wave packets to reduce interference. To suppress local noise in the average power envelope curve, the curve can be averaged and smoothed.

[0085] S42. Based on the obtained average power envelope curve, an exponential decay model is used for fitting to obtain the attenuation coefficient α. The calculation formula is as follows:

[0086] E(t)=E0e (-αt) (4)

[0087] Where E0 is the fitting parameter representing the initial power. To maintain a single decay pattern and improve the quantification accuracy of the decay coefficient, the start time for fitting the data is defined as the time of the first peak of the average power envelope; the end time is defined as the first inflection point of the average power envelope, that is, the time when the slope first reaches 0. If the average power envelope continuously decays throughout the recorded time range, all data after the maximum average power are used for fitting.

[0088] S5. Based on the wake wave attenuation coefficient obtained in step S4, a log-linear quantization model is used to obtain a grain size quantification result taking uncertainty into account. This step includes the following sub-steps:

[0089] S51. Obtain the mean of the logarithmic quantization results of the grain size according to the logarithmic linear quantization model. The logarithmic linear quantization model is as follows:

[0090] ln d=m1+m2 lnα (5)

[0091] Where d is the grain size quantification result, m1 and m2 are the first fitting parameter and the second fitting parameter of the log-linear quantization model obtained based on the wake wave experimental evaluation of the same material, and obey the multivariate normal distribution MVN(M, ∑), where M is the mean vector and ∑ is the covariance matrix.

[0092] S52. Considering the uncertainty of the model parameters, the first fitting parameter m1 and the second fitting parameter m2 are sampled according to the multivariate normal distribution MVN(M, ∑). According to the given attenuation coefficient α, the different combinations of the first fitting parameter m1 and the second fitting parameter m2 obtained by sampling are used to evaluate the logarithmic grain size based on formula (7), and then the probability density function of the logarithmic grain size is fitted using the normal distribution:

[0093]

[0094] Among them, μ and σ 2 are the mean and variance of the normal distribution, respectively. Based on the probability density function, we can obtain the probability distribution of the grain size quantification results, taking into account uncertainty. The mean of the probability distribution of grain size is the predicted value of grain size. At the same time, the prediction confidence level can be obtained based on the probability distribution of grain size, which can be used to evaluate the prediction accuracy. Specific embodiments

[0096] The present invention will be further described in detail below with reference to a specific case of a method for quantifying grain size of thick plate structure based on wake waves.

[0097] S1. The thick plate structure to be tested is a nickel-based high-temperature alloy specimen with a thickness of 5 mm. An ultrasonic quantification system for the grain size of the thick plate structure is built to perform ultrasonic testing on the thick plate structure to be tested. The specific process is as follows:

[0098] S11. Use 502 glue to stick a pair of ultrasonic transducers including an exciter and a receiver to the center of the surface of the thick plate structure to be tested to form a pulse echo detection configuration.

[0099] S12. The output of the control pulse generator (Tektronix, AFG 31022) generates a 3.5-cycle Hanning window modulated narrowband sine wave pulse as the input excitation signal of the ultrasonic transducer. At the same time, a synchronization signal is generated from the synchronization output and connected to the synchronization input of the oscilloscope (Tektronix, MDO3104).

[0100] S13. The center frequency of the excitation pulse is selected as 5MHz based on the thickness of the thick plate structure to be measured, the wave velocity and the estimated grain size range. The frequency-thickness product is 25MHz·mm, which can meet the conditions for the formation of wake waves in the structure and is sensitive to small grain sizes. The time domain waveform and spectrum of the excitation pulse g(t) are as follows: Figure 3 shown.

[0101] S14. Use the oscilloscope to synchronously collect the tail wave signal received by the ultrasonic transducer according to the synchronization signal of the synchronization input terminal as the trigger signal. In order to improve the signal-to-noise ratio of the signal, the collected ultrasonic signal is first processed by 128 time domain averages in the oscilloscope, and then transmitted to the computer for subsequent processing. The waveform and power spectrum density of the tail wave signal f(t) collected in the thick plate structure to be tested are as follows: Figure 4 shown.

[0102] S2. According to formula (1), the collected tail wave signal f(t) is cross-correlated with the excitation pulse g(t), and the crosstalk signal before 1.5μs is eliminated to obtain the preliminary noise reduction signal R(t). The result is as follows: Figure 5 As shown in Figure 2, the time domain waveform of the signal after preliminary noise reduction maintains the same key features as the original tail wave signal, preserving the components related to the input pulse. In the frequency domain, the signal retains the highest energy peak in the 3-6 MHz range, while other incoherent noise outside this range is relatively suppressed.

[0103] S3, such as Figure 6 As shown, according to formula (3), the initial noise reduction signal R(t) is subjected to variational mode decomposition to obtain six finite bandwidth intrinsic mode functions s i (t) (abbreviated as IMF) and the residual signal s r (t), i = 1, ..., 6. According to Figure 6 In the spectrum diagram of each limited bandwidth natural mode function shown, and the center frequency of the excitation pulse is 5 MHz, the third limited bandwidth signal I(t)=s3(t) with the smallest center frequency deviation is selected for subsequent analysis.

[0104] S4. Select the time window width T = 17.0 μs, which is ten times the original signal pulse packet interval. According to formula (5), with Δt = 0.02 μs as the interval, the average power of the finite bandwidth signal I(t) in the time window [t, t+T] is calculated at different times t, and after 5-point average smoothing, the average power envelope curve of the finite bandwidth signal is obtained, as shown in Figure 7 The average power envelope curve from 1.5μs to 19.72μs is intercepted and fitted using the exponential decay model shown in formula (6). The fitting results are shown in Figure 7 As shown, the attenuation coefficient α is obtained as 0.34μs -1 .

[0105] S5. In order to obtain the first fitting parameter m1 and the second fitting parameter m2 in the log-linear quantization model shown in formula (7), 10 5mm thick plate specimens T1-T10 of the same material with different grain sizes were prepared and the same ultrasonic testing steps as above were performed to obtain the corresponding attenuation coefficients. The maximum likelihood estimation of the first fitting parameter m1 and the second fitting parameter m2 of the model was performed in combination with the attenuation coefficient and grain size, and the estimated values ​​m1 = 7.14, m2 = 1.98 were obtained, and they obey the mean vector M = [7.14, 1.98] and the covariance matrix The first fitting parameter m1 and the second fitting parameter m2 are subjected to 5×10 6The logarithmic grain size is evaluated based on formula (7) using the combination of different first fitting parameters m1 and second fitting parameters m2 obtained by sampling, and then the probability density function of the logarithmic grain size is fitted using the normal distribution to obtain the probability distribution of the logarithmic grain size quantification result considering uncertainty. Figure 8 As shown. The mean and variance of the normal distribution are μ = 5.01 and σ respectively. 2 = 0.15. Using electron backscatter diffraction, the true grain size of the thick plate structure under test was determined to be 159.18 μm. It can be observed that the logarithmic value of the true grain size is within the 95% confidence interval of the probability density function, demonstrating the effectiveness and robustness of the log-linear model. Based on the maximum value of the probability density function, the average grain size predicted by the model is 149.60 μm, close to the true value of 159.18 μm, with a relative error of only 6.02%. This demonstrates that the proposed method can effectively and accurately quantify the grain size of thick plate structures.

[0106] The present invention proposes a method for quantifying grain size of thick plate structures based on wake waves. This method builds an ultrasonic grain size quantification system for thick plate structures, uses an ultrasonic transducer to pulse-excite the thick plate structure to be inspected, and collects wake wave signals. Based on the characteristics of the wake wave signal, a two-step signal noise reduction method is employed, including cross-correlation with the excitation pulse and signal filtering using a variational mode decomposition method to obtain a time-domain finite bandwidth signal. Subsequently, the attenuation law of the denoised finite bandwidth signal is analyzed based on the average power envelope to assess the attenuation coefficient of the wake wave in the thick plate structure. Finally, a logarithmic linear quantification model between the attenuation coefficient and grain size is used to quantify the uncertainty of the grain size. Compared to existing grain size quantification methods based on ultrasonic body waves and guided waves, this method is more suitable for evaluating thick plate structures, offering higher detection efficiency, lower analysis complexity, and ease of use. The resulting grain quantification results are highly accurate and robust.

[0107] Finally, it should be noted that the above embodiments are only intended to illustrate rather than limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the present invention can still be modified or replaced by equivalents. Any modification or partial replacement that does not depart from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for quantifying grain size of thick plate structure based on wake wave, characterized in that: It includes the following steps: S1. Build an ultrasonic quantification system for grain size of thick plate structures, apply pulse signal excitation to the thick plate structures and collect wake wave signals; S2. Perform cross-correlation operation on the collected tail wave signal f(τ) and the excitation pulse g(τ) to obtain a preliminary noise reduction signal. The calculation formula is as follows: Where R(t) is the initial noise reduction signal, τ is the time variable, and t is the time shift variable; S3, perform variational mode decomposition on the preliminary denoised signal R(t), and decompose the signal into k modes with different center frequencies ω i The bandwidth-limited intrinsic mode function s i (t), preliminary noise reduction signal R(t) and limited bandwidth intrinsic mode function s i (t) have the following relationship: Among them, s r (t) is the residual signal. According to the center frequency ω0 of the excitation pulse, the center frequency ω is selected from the k finite bandwidth natural mode functions. i The finite bandwidth intrinsic mode function s with the smallest deviation from ω0 i (t) as a bandwidth-limited signal I(t); S4. Fitting the attenuation coefficient using the average power envelope of the bandwidth-limited signal. This step includes the following sub-steps: S41. For different values ​​of t, calculate the average power of the bandwidth-limited signal I(t) within the time window [t, t+T] with a width of T, and obtain the average power envelope curve of the bandwidth-limited signal. The calculation formula is as follows: Where u is the time variable in the time window [t, t+T], and E(t) is the average power envelope curve; S42, based on the obtained average power envelope curve, fitting using an e-exponential decay model to obtain an attenuation coefficient α; The calculation formula of the attenuation coefficient α is as follows: E(t)=E0e (-αt) (4) Where E0 is the fitting parameter representing the initial power; the starting time of the data used for fitting is the time of the first peak of the average power envelope; the ending time is the first inflection point of the average power envelope, that is, the time when the slope first reaches 0; if the average power envelope continues to decay over the entire recorded time range, all data after the maximum average power are used for fitting; S5. Based on the wake wave attenuation coefficient obtained in step S4, a log-linear quantization model is used to obtain a grain size quantification result taking uncertainty into account. This step includes the following sub-steps: S51, constructing a logarithmic linear quantization model, and obtaining a logarithmic quantization result lnd of the grain size according to the logarithmic linear quantization model; S52. Calculate the probability density function of the logarithmic grain size, obtain multiple sets of logarithmic grain sizes using a logarithmic linear quantization model, and fit the probability density function of the logarithmic grain size using a normal distribution: Among them, μ and σ 2 are the mean and variance of the normal distribution respectively. According to the probability density function, the probability distribution of the predicted grain size considering the uncertainty is obtained. The mean of the probability distribution of the grain size is the predicted value of the grain size.

2. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: The log-linear quantization model in step S51 is as follows: lnd=m1+m2 lnα (5) Among them, d is the grain size quantification result, m1 and m2 are the first fitting parameter and the second fitting parameter of the log-linear quantization model obtained based on the wake wave experimental evaluation of the same material, and obey the multivariate normal distribution MVN(Μ,Σ), where Μ is the mean vector and Σ is the covariance matrix.

3. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: In step S52, considering the uncertainty of the model parameters, the first fitting parameter m1 and the second fitting parameter m2 are sampled according to the multivariate normal distribution MVN(Μ,Σ), and based on the solved attenuation coefficient α, the logarithmic grain size is obtained by using the combination of different first fitting parameters m1 and second fitting parameters m2 obtained by sampling using the logarithmic linear quantization model.

4. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: In step S1, the pulse signal is used to excite the thick plate structure to be measured and the wake wave signal is collected, which specifically includes the following steps: S11, placing an ultrasonic transducer on the target area surface of the thick plate structure to be measured; S12, controlling the output end of the pulse generator to generate a narrowband sinusoidal wave pulse as an input excitation signal for the ultrasonic transducer, and simultaneously generating a synchronization signal from the synchronization output end and connecting the synchronization signal to the synchronization input end of the oscilloscope; S13. The center frequency of the excitation pulse is determined based on the thickness of the thick plate structure to be measured, the wave velocity and the estimated grain size range, so that the frequency-thickness product is greater than 15 MHz·mm; S14. Using an oscilloscope, based on the synchronization signal of the synchronization input terminal as a trigger signal, synchronously collects the tail wave signal received by the ultrasonic transducer and transmits it to the upper controller.

5. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: The tail wave signal used for the cross-correlation calculation in step S2 is the signal after the initial crosstalk portion of the signal is removed.

6. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: The constrained variational problem to be constructed for variational modal decomposition in step S3 is: Where δ(t) is the Dirac delta function, j is the imaginary unit, and i = 1,…,k. By introducing the quadratic penalty term β and the Lagrange multiplier λ, the constrained problem is transformed into the following unconstrained problem: Among them, L({s i },{ω i },λ) is the augmented Lagrangian function, and the optimization problem is solved iteratively to obtain k finite bandwidth intrinsic mode functions s i (t).

7. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: In step S4, different times t for evaluating the average power are selected at a certain time interval Δt.

8. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: The time window width T used for evaluating the average power in step S4 includes a plurality of reflected wave packets.

9. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: In step S4, the curve is averaged and smoothed, thereby suppressing local noise in the average power envelope curve.

10. The method for quantifying grain size of thick plate structure based on wake wave according to claim 1, characterized in that: In step S5 , the first fitting parameter and the second fitting parameter of the model and their respective distributions are determined using a plurality of thick plate specimens having the same thickness and material as the thick plate structure to be measured but with different grain sizes.

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